The present invention relates generally to methods of encoding signals to provide specifiable autocorrelation properties and in particular to methods for encoding signals to provide low autocorrelation at predetermined offsets and low predictability to unauthorized recipients, in order to reduce the effects of multipath, noise and electronic countermeasures (ECM).
There are many applications where it is desirable to encode signals such that the encoded signals have certain specifiable autocorrelation properties. Typical of such applications are those where it is required to synchronize a receiver to a received signal, or to measure its time of arrival at the receiver. For example, radar is one application where it is desirable to be able to accurately determine the time of arrival of the return signals reflected from targets, in order to measure the target's range from the radar. Often this must be done in presence of noise or clutter caused by reflections from the ground or other objects, which obscure the return signal and make the measurement difficult.
A convenient way of overcoming the undesirable effects of noise and to improve the accuracy of the measurement is to perform a correlation process, since it is known that the autocorrelation function has a maximum value at zero time offset. A correlation process can be implemented by multiplying the return signal by a delayed replica of the transmitted signal, which is stored in the receiver, and performing an integration. When the delay is adjusted to equal the total round trip time of the signal from the radar to the target, the correlation value will be a maximum. At delays other than those equal to the exact round trip time of the signal, the offset will be non-zero and the correlation value will be less than the maximum. Thus, the round trip time can be easily determined by adjusting the delay until the correlation value is maximized.
Another application where signals having good autocorrelation properties are desirable, is in navigational systems such as LORAN, where the exact time of arrival of signals from several known locations must be measured with respect to a reference time. From these measurements, the location of the receiver can be determined. Since these navigational signals are often corrupted by noise and multipath, these time of arrival measurements can be difficult to make accurately. For example, in LORAN, transmitted signals can be reflected from various atmospheric layers to produce skywaves, which can arrive at the receiver overlapping the direct, ground wave signal. Furthermore, these skywave signals may at times have a greater strength than the direct wave. This results in a self-jamming effect. It is therefore necessary to be able to discriminate between skywaves and ground waves. An autocorrelation process is a convenient manner of accomplishing this.
Receivers capable of performing autocorrelation functions are well known. For example, see U.S. Pat. No. 3,868,691 to Miller et al., which discloses an automatic 2-step correlation receiver for LORAN. Another method of discriminating between the direct waves and skywaves in LORAN is disclosed in U.S. Pat. No. 3,858,216 to DeVaul, wherein the signal amplitude of received waves is determined by detecting the slope of the first derivative, and skywave rejection is performed by detecting the timing between various portions of the received signal envelope. U.S. Pat. No. 3,174,151 to Abourezk, discloses a system for detecting synchronization on skywaves by detecting the presence of signals received just prior to the signal on which the receiver is synchronized. It is based on the principle that since skywaves travel a greater distance than ground waves, they arrive at a receiver later in time than the ground waves. U.S. Pat. No. 3,411,089 to Gicca, discloses a system for coding transmitted signals with a multiplicity of frequencies, in patterns to represent the information being transmitted, in order to reduce the effectiveness of jamming, and to enhance the detectability of the signals in the presence of noise.
Since the autocorrelation function has a maximum value at zero offset, the operation of correlation receivers can be enhanced by encoding the transmitted signals such that at non-zero offsets the autocorrelation values are small with respect to autocorrelation value at zero offset. Ideally, it is desirable that the transmitted signal be coded such that it has small absolute non-cyclic autocorrelation function values at all except zero offsets. Thresholds could then be easily established and zero offset determined whenever the autocorrelation value exceeds the threshold. Unfortunately, binary words having this property are rare. A coding scheme currently used by LORAN C employs complementary pairs of codewords. In this scheme, two words are transmitted such that when individually autocorrelated, the values obtained at the same non-zero offset sum to zero. At zero offset, the summed values of the autocorrelation functions are double that of a single word. This improves the determination of the time of arrival of the ground wave signal and effectively eliminates the problem caused by skywaves, since their contribution to the correlations sums to zero.
Complementary pair codewords may or may not exist, however, depending upon the number of bits required. For example, they are known to exist if the number of bits in the word is of the form 2.sup.a+1 5.sup.b 13.sup.c, where a, b and c are non-negative integers. The LORAN D system proposes to use 16-bit words. It is therefore possible to find such complementary pair codewords for use on LORAN D, and in fact there are exactly 768 such pairs.
In addition to encoding signals to provide good auto-correlation properties, it is often desirable to encode signals so that they have low predictability to unauthorized recipients. This renders the signals less susceptible to electronic countermeasures, such as jamming, which may be employed by a hostile military force during an armed confrontation. In order to provide low predictability, it is necessary that the codewords have a very low redundancy and a long mean time to certainty. The redundancy of codewords is determined by finding the difference between the probabilities of right and wrong guesses for each bit of a codeword, given all previous codewords. Mean time to certainty of a codeword is determined by measuring the number of bits which must be observed, on the average, before the remainder of the codeword is completely determined.
While the coding of LORAN D using complementary pairs provides desirable autocorrelation properties, these complementary pairs have unacceptably high levels of predictability, which renders them highly susceptible to jamming or other ECM attacks. For example, it can be shown that the first word of a 16-bit complementary pair has an expected redundancy of 72/3 bits, i.e., one expects to guess correctly 11 5/6 of the 16 bits. Given the first word the expected redundancy of the second word is 14-bits, i.e., one expects 15 correct guesses out of 16 bits. Thus the total redundancy is 212/3 bits out of 32, a rather large value. The mean time to certainty of the first word of a pair is 101/3 bits, and given the first word, the mean time to certainty of the second word is a mere 2 5/6 bits.
It is desirable therefore to provide a coding scheme which simultaneously has good autocorrelation properties in order to provide good multipath rejection, while at the same time having low predictability, in order to reduce the effectiveness of ECM attacks. Accordingly, it is an object of the invention to provide an improved method and apparatus for coding which has these desirable properties.
There are other applications where it may be desirable to provide codewords having specifiable autocorrelation properties, i.e., a high correlation value, at predetermined offsets, whether or not it is also desirable to provide low predictability. Consequently, it is additionally an object of the invention to provide a method and apparatus for coding in which the codewords have specifiable autocorrelation properties.
An apparatus for generating n-bit codewords, X, for encoding a signal to provide predetermined autocorrelation properties at an offset of j bits, which accomplishes these objectives and has other advantages may include means for generating (n-j)-bit codewords, y.sub.j, said codewords having a predetermined ratio of logical 1's to logical 0's and said codewords being the jth difference of said X codewords, and means for combining the n-j bits of said y.sub.j codewords with j arbitrary bits to form said n-bit codewords X.
A method of constructing n-bit codewords, X, for encoding a signal for transmission to provide signal properties facilitating rejection at a receiver of multipath signal waves arriving at the receiver delayed with respect to direct waves, which accomplishes these and other objectives, may include the steps of generating a sequence of (n-j)-bit codewords, y.sub.j, where the expected delay between the time of arrival of the direct and the multipath signal waves is j bits, the y.sub.j codewords being the jth difference of the X codewords, and the y.sub.j codewords further being constant ratio codewords having a ratio of logical 1's to logical 0's approximately equal to one; and combining the y.sub.j codewords with j arbitrary bits to form the X codewords.